On the magnetic field evolution in shell-like supernova remnants

In this paper we apply and discuss a method for the determination of the magnetic field ($H$) evolution in supernova remnants (SNRs) from radio luminosity at given frequency $\nu$ to diameter ($L_\mathrm{\nu}-D$) correlation. We assumed that $H$ evolves as $H\propto D^{-\delta}$, where $D$ is the diameter of the remnant. Value $\delta\approx1.2$ is obtained under the equipartition assumption from the equations for revised equipartition calculation (REC) and by using the data sample from the nearby starburst galaxy M82. We try to investigate whether or not SNRs in M82 are in the equipartition state. This is done by comparison of our empirically obtained $\delta$ with the theoretical value expected for the equipartition conditions. Inconsistence between the value obtained for equipartition conditions and adiabatic expansion $(\delta=1.5)$ and the value empirically obtained herein, can be explained mainly by the influence of sensitivity selection effects which tend to flatten the slope of the $L_\nu-D$ relations for extragalactic samples.